Approximate Subgradient Methods for Lagrangian Relaxations on Networks

Nonlinear network flow problems with linear/nonlinear side con- straints can be solved by means of Lagrangian relaxations. The dual problem is the maximization of a dual function whose value is estimated by minimizing approximately a Lagrangian function on the set defined by the network constraints. We study alternative stepsizes in the approximate subgradient methods to solve the dual problem. Some basic convergence results are put forward. Moreover, we compare the quality of the computed solutions and the efficiency of these methods.

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